Let $X$ be a normal Hausdorff space. Let $A_1$, $A_2$, and $A_3$ be closed subsets of $X$ which are pairwise disjoint. Then there always exists a continuous real valued function $f$ on $X$ such that $f(x) = a_i$ if $x$ belongs to $A_i$, $i=1,2,3$
iff each $a_i$ is either 0 or 1.
iff at least two of the numbers $a_1$, $a_2$, $a_3$ are equal.
for all real values of $a_1$, $a_2$, $a_3$.
only if one among the sets $A_1$, $A_2$, $A_3$ is empty.